{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "73a03900",
   "metadata": {},
   "source": [
    "# Qini curves with multiple costly treatment arms\n",
    "\n",
    "This notebook shows approaches to evaluating multi-armed CATE estimators from `causalML` with the Multi-Armed Qini metric available in the `maq` package (available at https://github.com/grf-labs/maq).\n",
    "\n",
    "\n",
    "This metric is a generalization of the familiar *Qini curve* to settings where we have multiple treatment arms available, and the cost of assigning treatment can vary by both unit and treatment arm according to some known cost structure. At a high level, this metric essentially allows you to quantify the value of targeting with more treatment arms by undertaking a cost-benefit exercise that uses your CATE estimates to assign the arm to the unit that is most cost-beneficial at various budget constraints.\n",
    "\n",
    "This notebook gives a brief overview of the statistical setup and a walkthrough with a simple simulated example. \n",
    "\n",
    "\n",
    "To use this functionality, you first have to install the `maq` Python package from GitHub. The latest source release can be installed with:"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0a633fa7",
   "metadata": {},
   "source": [
    "```\n",
    "pip install \"git+https://github.com/grf-labs/maq.git#egg=maq&subdirectory=python-package\"\n",
    "```"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "6253bbf7",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Treatment effect estimators (R-learner with Causal ML + XGBoost)\n",
    "from causalml.inference.meta import BaseRRegressor\n",
    "from xgboost import XGBRFRegressor\n",
    "\n",
    "# Generalized Qini curves\n",
    "from maq import MAQ, get_ipw_scores\n",
    "\n",
    "import numpy as np\n",
    "np.random.seed(42)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "157b0814",
   "metadata": {},
   "source": [
    "## Statistical setup\n",
    "\n",
    "Let $k = 1, \\ldots K$ denote one of $K$ mutually exclusive and costly treatment arms and $k = 0$ a (costless) control arm.  Let $Y_i(k)$ denote the potential outcome in the $k$-th arm for unit i, and $X_i$ a set of observable characteristics.\n",
    "\n",
    "Let the function $\\hat \\tau(\\cdot)$ be an estimate of the conditional average treatment effect (CATE) obtained from a training set, where the $k$-th element estimates\n",
    "$$\n",
    "\\tau_k(X_i) = E[Y_i(k) - Y(0) ~|~ X_i].\n",
    "$$\n",
    "\n",
    "The Qini curve $Q(B)$ quantifies the value of assigning treatment in accordance with our estimated function $\\hat \\tau(\\cdot)$ over different values of a budget constraint $B$. With a **single treatment arm** $K=1$ we can formalize this as\n",
    "$$\n",
    "Q(B) = E[ \\pi_B(X_i)\\left( Y_i(1) - Y_i(0) )\\right] = E[\\pi_B(X_i) \\tau(X_i)],\n",
    "$$\n",
    "\n",
    "\n",
    "where $\\pi_B(X_i) \\in \\{0, 1\\}$ is the *policy* that assigns treatment (=1) to those units *predicted* by $\\hat \\tau(\\cdot)$ to benefit the most such that on average we incur a cost of at most B. If we let $C(\\cdot)$ denote our known cost function (e.g. $C(X_i) = 4.2$ means assigning the $i$-th unit the treatment costs 4.2 on some chosen cost denomination), then $\\pi_B$ is going to look like\n",
    "$$\n",
    "\\pi_B = argmax_{\\pi} \\left\\{ E[\\pi_B(X_i) \\hat \\tau(X_i)] : E[\\pi_B(X_i) C(X_i)] \\leq B  \\right\\}\n",
    "$$\n",
    "\n",
    "While slightly daunting written down formally, it turns out expressing $\\pi_B$ is quite simple: it essentially reduces to a thresholding rule: for a given $B$, treat the units where the predicted cost-to-benefit ratio $\\frac{\\hat \\tau(X_i)}{C(X_i)}$ is above a cutoff. The  Qini curve can be used to quantify the value, as measured by the expected gain over assigning each unit the control arm when using the estimated function $\\hat \\tau(\\cdot)$ with cost structure $C(\\cdot)$ to allocate treatment,\n",
    "as we vary the available budget $B$.\n",
    "\n",
    "With **multiple treatment arms** $K > 1$, our object of interest, the Qini curve, is the same, we just need to add an inner product $\\langle,\\rangle$ to the notation\n",
    "$$\n",
    "Q(B) = E[\\langle \\pi_B(X_i),~ \\tau(X_i) \\rangle],\n",
    "$$\n",
    "to denote that $\\pi_B(X_i)$ now is a $K$-length selection vector with 1 in the $k$-th entry if we predict that it is optimal to assign the $i$-th unit that arm at the given budget constraint. Similarly to above, $\\pi_B$ takes the following form\n",
    "$$\n",
    "\\pi_B = argmax_{\\pi} \\left\\{ E[\\langle \\pi_B(X_i),~ \\hat \\tau(X_i)\\rangle] : E[\\langle \\pi_B(X_i),~ C(X_i)\\rangle] \\leq B  \\right\\}.\n",
    "$$\n",
    "Expressing $\\pi_B$ is more complicated now, as for each budget constraint $B$, $\\pi_B$ has to make decisions of the form \"should I assign the $i$-th unit an initial arm, or if the $j$-th unit had already been assigned an arm: should I upgrade this person to a costlier but more effective arm?\". It turns out that it is possible to express $\\pi_B$ as a thresholding rule (for details we refer to this [paper](https://arxiv.org/abs/2306.11979)), yielding tractable ways to construct Qini curves for multi-armed treatment rules."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f441c629",
   "metadata": {},
   "source": [
    "## Example\n",
    "\n",
    "### Fitting a CATE function on a training set\n",
    "\n",
    "Generate some simple (synthetic) data with $K=2$ treatment arms, where the second arm is more effective on average."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "509021f8",
   "metadata": {},
   "outputs": [],
   "source": [
    "n = 20000\n",
    "p = 5\n",
    "\n",
    "# Draw a treatment assignment from {0, 1, 2} uniformly\n",
    "W = np.random.choice([0, 1, 2], n)\n",
    "# Generate p observable characteristics where some are related to the CATE\n",
    "X = np.random.rand(n, p)\n",
    "Y = X[:, 1] + X[:, 2]*(W == 1) + 1.5*X[:, 3]*(W == 2) + np.random.randn(n)\n",
    "# (in this example, the true arm 2 CATE is 1.5*X[:, 3])\n",
    "\n",
    "# Generate a train/test split\n",
    "n_train = 15000\n",
    "ix = np.random.permutation(n)\n",
    "train, test = ix[:n_train], ix[n_train:]"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d243adf8",
   "metadata": {},
   "source": [
    "Obtain $\\hat \\tau(\\cdot)$ by fitting a CATE estimator on the training set (using an *R-learner*, for example).\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "fb43f8c9",
   "metadata": {
    "scrolled": true
   },
   "outputs": [],
   "source": [
    "# Use known propensities (1/3)\n",
    "W_hat = np.repeat(1 / 3, n_train)\n",
    "propensities = {0: W_hat, 1: W_hat, 2: W_hat}\n",
    "\n",
    "tau_function = BaseRRegressor(XGBRFRegressor(), random_state=42)\n",
    "tau_function.fit(X[train, :], W[train], Y[train], propensities)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c20d17fc",
   "metadata": {},
   "source": [
    "### Estimating Q(B) on a test set\n",
    "\n",
    "At a high level, there are two tasks associated with estimating a Qini curve $Q(B)$. The first one is estimating the underlying policy $\\pi_B$, and the second is estimating the value of this policy.\n",
    "\n",
    "As mentioned in the previous section, with multiple costly treatment arms, the policy $\\pi_B$ is more complicated to compute than in the single-armed case, since given a treatment effect function (obtained from some training set) and a cost structure, we need to figure out which arm to assign to which unit at every budget constraint. The maq package performs this *first* step with an algorithm that gives the path of multi-armed policies $\\pi_B$.\n",
    "\n",
    "For the *second* step of estimating the value of this policy, we need to construct a matrix of suitable evaluation *scores* (that we denote by $\\Gamma$) that have the property that when averaged they act as treatment effect estimates.\n",
    "\n",
    "If we know the treatment randomization probabilities $P[W_i=k~|~X_i]$, it turns out that constructing these scores is easy: we can simply use inverse-propensity weighting (IPW). With $K$ treatment arms, the scores for the $k$-th arm\n",
    "then takes the following form\n",
    "\n",
    "$$\n",
    "\\Gamma_{i,k} = \\frac{1(W_i=k)Y_i}{P[W_i=k~|~X_i]} - \\frac{1(W_i=0)Y_i}{P[W_i=0~|~X_i]},\n",
    "$$\n",
    "\n",
    "where $W_i$ and $Y_i$ are the treatment assignment and observed outcome for test set unit i. An estimate of the ATE for the $k$-th arm is given by the average of these scores: $\\frac{1}{n_{test}} \\sum_{i=1}^{n_{test}} \\Gamma_{i,k}$. An IPW-based estimate of $Q(B)$ is going to be an average of these scores that \"matches\" the underlying policy prescription $\\pi_B$.\n",
    "\n",
    "the `maq` package has a simple convenience utility `get_ipw_scores` that can be used to construct these via IPW (which by default assumes the arms have uniform assignment probabilities $\\frac{1}{K+1}$).\n",
    "\n",
    "*Note*: if the randomization probabilities are not known (as could be the case in an observational setting), then a more robust alternative to form the scores via plugging in estimates of the propensities into the expression above, is to use augmented inverse-propensity weighting (AIPW), yielding a doubly robust estimate of the Qini curve. This approach is not covered here, for details we refer to the [paper](https://arxiv.org/abs/2306.11979).\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "f674c2aa",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Construct an n_test*K matrix of evaluation scores \n",
    "IPW_scores = get_ipw_scores(Y[test], W[test])\n",
    "\n",
    "# Predict CATEs on the test set\n",
    "tau_hat = tau_function.predict(X[test, :])\n",
    "\n",
    "# Specify our cost structure, \n",
    "# assume the cost of assigning each unit the first arm is 0.2\n",
    "# and the cost of assigning each unit the second more effective arm is 0.5\n",
    "# (these can also be array-valued if costs vary by unit)\n",
    "cost = [0.2, 0.5]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "0b66c61b",
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Start by fitting a baseline Qini curve that only considers the average treatment effects and costs\n",
    "qini_baseline = MAQ(target_with_covariates=False, n_bootstrap=200)\n",
    "qini_baseline.fit(tau_hat, cost, IPW_scores)\n",
    "\n",
    "qini_baseline.plot()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ee3ec40c",
   "metadata": {},
   "source": [
    "This curve has a kink at $B=0.2$: the first segment traces out the ATE of the lower cost arm, and the second segment the ATE of the higher cost but on average more effective arm. Points on this curve represents the average benefit per unit when targeting an arbitrary group of units.\n",
    "\n",
    "For example, at an average spend of 0.2 our gain (along with standard errors) is equal to the arm 1 ATE of"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "b2f204ef",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(0.49665725358631685, 0.047913821952266705)"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "qini_baseline.average_gain(0.2)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3027ca3d",
   "metadata": {},
   "source": [
    "Next, we fit a Qini curve for arm 1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "174fa773",
   "metadata": {},
   "outputs": [],
   "source": [
    "tau_hat_1 = tau_hat[:, 0]\n",
    "cost_1 = cost[0]\n",
    "IPW_scores_1 = IPW_scores[:, 0]\n",
    "\n",
    "qini_1 = MAQ(n_bootstrap=200).fit(tau_hat_1, cost_1, IPW_scores_1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "a37d3e17",
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "qini_baseline.plot(show_ci=False)\n",
    "# Plot curve with 95% confidence bars\n",
    "qini_1.plot(color=\"blue\", label=\"arm 1\")\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b2556d78",
   "metadata": {},
   "source": [
    "The Qini curve for this arm plateaus at a spend of around"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "e4ce759e",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.168840000000009\n"
     ]
    }
   ],
   "source": [
    "print(qini_1.path_spend_[-1])"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b7088967",
   "metadata": {},
   "source": [
    "which means that at this spend level we have given treatment to all units predicted to benefit from treatment (that is, `tau_hat_1` is > 0). We can read off estimates and std errors from the curve, for example at a spend of $B=0.1$ per unit, the estimated average treatment effect per unit is"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "8d3e05a9",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(0.36935574662263526, 0.037401976389534526)"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "qini_1.average_gain(0.1)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c831e214",
   "metadata": {},
   "source": [
    "(these standard errors are conditional on the estimated function $\\hat \\tau(\\cdot)$ and quantify test set uncertainty in estimating the Qini curve).\n",
    "\n",
    "We can assess the value of targeting with arm 1 at various spend levels by estimating the vertical difference between the blue and black line. Let's call the Qini curve for arm 1 $Q_1(B)$ and the Qini curve for the baseline policy $\\overline Q(B)$. At $B=0.1$, an estimate of $Q_1(0.1) - \\overline Q(0.1)$ is"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "0e33191d",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(0.12102711982945671, 0.024068445449392815)"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "est, std_err = qini_1.difference_gain(qini_baseline, 0.1)\n",
    "est, std_err"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "229c0aea",
   "metadata": {},
   "source": [
    "That is, at a budget of 0.1 per unit a 95% confidence interval for the increase in gain when targeting with the given arm 1 CATE function over random targeting is"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "bde64358",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[0.0738529667486468, 0.16820127291026662]"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "[est - 1.96*std_err, est + 1.96*std_err]"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "89a85f21",
   "metadata": {},
   "source": [
    "(points on aribtrary curves can be compared with the `difference_gain` method, yielding paired standard errors that account for the correlation between Qini curves fit on the same test data).\n",
    "\n",
    "Similarily, we can estimate a Qini curve $Q_2(B)$ for the second costlier arm"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "73816820",
   "metadata": {},
   "outputs": [],
   "source": [
    "tau_hat_2 = tau_hat[:, 1]\n",
    "cost_2 = cost[1]\n",
    "IPW_scores_2 = IPW_scores[:, 1]\n",
    "\n",
    "qini_2 = MAQ(n_bootstrap=200).fit(tau_hat_2, cost_2, IPW_scores_2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "f3dc13a1",
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "qini_baseline.plot(show_ci=False) # Leave out CIs for legibility\n",
    "qini_1.plot(color=\"blue\", label=\"arm 1\", show_ci=False)\n",
    "qini_2.plot(color=\"red\", label=\"arm 2\", show_ci=False)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d72c8e60",
   "metadata": {},
   "source": [
    "Finally, we can see what a Qini curve $Q(B)$ using both arms looks like."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "2cbc3082",
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "qini_ma = MAQ(n_bootstrap=200).fit(tau_hat, cost, IPW_scores)\n",
    "\n",
    "qini_baseline.plot(show_ci=False)\n",
    "qini_1.plot(color=\"blue\", label=\"arm 1\", show_ci=False)\n",
    "qini_2.plot(color=\"red\", label=\"arm 2\", show_ci=False)\n",
    "qini_ma.plot(color=\"green\", label=\"both arms\", show_ci=False)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b8aee845",
   "metadata": {},
   "source": [
    "Qini curves for single-armed treatment rules allow for assessing the value of targeting with a specific arm or targeting function. The generalization of the Qini to multiple treatment arms allows us to also assess the value of targeting with a combination of arms.\n",
    "\n",
    "At $B=0.3$, the estimated increase in gain when targeting with both arms over using only the second arm, $Q(0.3) - Q_2(0.3)$, is"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "33fb9348",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(0.17003364056661086, 0.036733311977033105)"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "qini_ma.difference_gain(qini_2, 0.3)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ae691ca3",
   "metadata": {},
   "source": [
    "In this example, a multi-armed policy achieves a larger gain by assigning the treatment that is most cost-beneficial to each test set unit. The underlying policy $\\pi_B$ looks like"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "529d4802",
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[0., 1.],\n",
       "       [0., 1.],\n",
       "       [1., 0.],\n",
       "       ...,\n",
       "       [1., 0.],\n",
       "       [0., 1.],\n",
       "       [0., 1.]])"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "qini_ma.predict(0.3)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4dbe9ecf",
   "metadata": {},
   "source": [
    "where rows correspond to $\\pi_B(X_i)$, where the $k$-th column contains a 1 if it is optimal to assign this arm to the $i$-th unit at the given spend (and all entries 0 if the control arm is assigned). An alternative representation of the policy is to take values in the treatment arm set {0, 1, 2}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "d193b972",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([2, 2, 1, ..., 1, 2, 2])"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "qini_ma.predict(0.3, prediction_type=\"vector\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3c2ba17c",
   "metadata": {},
   "source": [
    "In addition to comparing points on different Qini curves, we can also compare across a range of spend levels by estimating an area between two curves up to a maximum $\\overline B$. An estimate and standard error of the area between the green and red curves up to $\\overline B=0.5$, the integral $\\int_{0}^{0.5} (Q(B) - Q_2(B))dB$, is"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "934a6f62",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(0.12548196750671803, 0.02945344768121884)"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "qini_ma.integrated_difference(qini_2, 0.5)"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.9.18"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}
